Endomorphism algebras of factors of certain hypergeometric Jacobians

Xue, Jiangwei; Yu, Chia-Fu

doi:10.1090/tran/6330

Endomorphism algebras of factors of certain hypergeometric Jacobians
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by Jiangwei Xue and Chia-Fu Yu PDF

Trans. Amer. Math. Soc. 367 (2015), 8071-8106 Request permission

Abstract:

We classify the endomorphism algebras of factors of the Jacobians of certain hypergeometric curves over a field of characteristic zero. Other than a few exceptional cases, the endomorphism algebras turn out to be either a cyclotomic field $E=\mathbb {Q}(\zeta _q)$, or a quadratic extension of $E$, or $E\oplus E$. This result may be viewed as a generalization of the well known results of the classification of endomorphism algebras of elliptic curves over $\mathbb {C}$.

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